On a homogenization technique for singular integrals

Abstract

We study homogenization by Γ-convergence of functionals of type

∫_ΩW(x/ε,∇ϕ(x)) dx,

where Omega⊂R^N is a bounded open set, ϕ∈W^1,p(Omega;R^m) and p>1, when the 1-periodic integrand W :R^N×M^m×N→[0,+∞] is not of p-polynomial growth. Our homogenization technique can be applied when m=N and W has a singular behavior of type W(x,ξ)→+∞ as det ξ→0. However, our technique is not consistent with the constraint W(x,ξ)=+∞ if and only if det ξ≤0.